So I was going to attempt to explain this, then I realized that I am somewhat limited in my knowledge of both. So I did a google and found some good info that seems to make sense. Here is an excerpt from what I found.
"
I'm not knowledgeable about the engineering aspects such as the cost of one
Compared to the other. However, as the names imply deionized water is water
that has been passed through a column or membrane to remove ions present. If
it is of the type used in homes, it is not truly a de-ionizer, removing all
ions, but rather an ion exchange column that exchanges polyvalent ions such
as Mg++ and Ca++ for Na+ ions. A de-ionizing column will not remove nonionic
organic substances from the water.
In contrast, distilled water is actually boiled in a still and the
condensate collected and distributed. Distillation removes both ionic and
nonionic organic contaminants.
Either method will require periodic regeneration, in the case of a
deionizer, or cleaning in the case of a still. I think you will have to
weigh the cost of maintenance and the required capacity needed before making
your decision."
Vince Calder - as found at
http://www.newton.dep.anl.gov/askasc.../chem00223.htm
It's about time I did a little research on this one myself. I guess it really makes sense that using condensation would eliminate a broader range of impurities. As for the quantity removed given either method who knows....